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Question #18188

Let R be a finite-dimensional k-algebra which splits over k. Show that, for any field K ⊇ k, rad (RK) = (rad R)K.

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**1.**Let M,N be finite-dimensional modules over a finite-dimensional k-algebra R. For any field K &su**2.**For any nonzero ring k and any group G, show that the group ring kG is von Neumann regular iff k is**3.**Show that statement "for any von Neumann regular ring k, any finitely generated submodule M**4.**For any von Neumann regular ring k, show that any finitely generated submodule M of a projective k-m**5.**For any von Neumann regular ring k, show that any finitely generated submodule M of a projective k-m**6.**Show that, if G can be right ordered, then, for any domain k, A = kG has only trivial units and is a**7.**For any group G, let Δ(G) = {g ∈ G: [G : CG(g)] < ∞}, and &D

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